7n^2+33n+28=8

Solution for 7n^2+33n+28=8 equation:

7n^2+33n+28=8

We move all terms to the left:

7n^2+33n+28-(8)=0

We add all the numbers together, and all the variables

7n^2+33n+20=0

a = 7; b = 33; c = +20;
Δ = b2-4ac
Δ = 332-4·7·20
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-23}{2*7}=\frac{-56}{14}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+23}{2*7}=\frac{-10}{14}
=-5/7
$